Quiz : Maîtrisez les relations d’ordre en Terminale Mathématiques

Question 1 sur 10 10:00

[{"id":62802,"question":"Parmi les relations suivantes, laquelle définit un ordre partiel sur l’ensemble {1, 2, 3} ?","option_a":"A. a ≤ b","option_b":"B. a \u003C b","option_c":"C. a divise b","option_d":"D. a = b","option_e":"","option_f":"","bonne_reponse":"C","explication":"La relation 'a divise b' est réflexive, antisymétrique et transitive, mais tous les éléments ne sont pas comparables (ex: 2 et 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62803,"question":"Un ensemble ordonné est toujours fini.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un ensemble ordonné peut être infini, comme l’ensemble des réels avec l’ordre usuel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62804,"question":"Quelle est la borne inférieure de l’intervalle ]-2, 5] ?","option_a":"A. -2","option_b":"B. 5","option_c":"C. -∞","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La borne inférieure est la plus grande valeur inférieure à tous les éléments de l’intervalle, ici -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62805,"question":"Si un ensemble admet une borne supérieure, celle-ci est toujours unique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, la borne supérieure est unique si elle existe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62806,"question":"Parmi les ensembles suivants, lequel est totalement ordonné par la relation ≤ ?","option_a":"A. {1, 2, 3}","option_b":"B. L’ensemble des parties d’un ensemble","option_c":"C. L’ensemble des réels","option_d":"D. L’ensemble des entiers pairs","option_e":"","option_f":"","bonne_reponse":"C","explication":"L’ensemble des réels est totalement ordonné par ≤, contrairement aux autres options.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62807,"question":"La relation 'a ≤ b' sur l’ensemble des entiers naturels est-elle une relation d’ordre ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car elle est réflexive, antisymétrique et transitive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62808,"question":"Quel est le majorant de l’ensemble {x ∈ ℝ | 0 ≤ x ≤ 1} ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 2","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"B","explication":"1 est un majorant car tous les éléments de l’ensemble sont inférieurs ou égaux à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62809,"question":"Un ensemble peut avoir plusieurs bornes supérieures distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Non, la borne supérieure est unique si elle existe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62810,"question":"Parmi les relations suivantes, laquelle est une relation d’ordre sur ℝ ?","option_a":"A. a + b","option_b":"B. a ≤ b","option_c":"C. a × b","option_d":"D. a - b","option_e":"","option_f":"","bonne_reponse":"B","explication":"La relation 'a ≤ b' est une relation d’ordre sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62811,"question":"Si un ensemble est borné supérieurement, sa borne supérieure appartient nécessairement à l’ensemble.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Non, comme dans l’exemple de l’intervalle ]0,1[ où la borne supérieure est 1 ∉ ]0,1[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]